## Probability Distribution

Probability Distribution is defined as a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

Let us consider an Example of tossing a coin, the possible outcomes are head or a tail ,

The probability of getting a head is \( \frac{1}{2} \) ,similarly for getting a tail is also the same which is \( \frac{1}{2} \).

In the case of rolling a die, the possible outcomes is getting a number from 1 to 6,

And for getting “1” after rolling a die is \( \frac{1}{6} \) , similarly for getting “2”,”3”,”4”,”5”,”6” is also the same which is \( \frac{1}{6} \) respectively .

A probability distribution function is formally defined by a Cumulative Distribution Function(CDF) ,

The CDF of a real-valued random variable \( X \) ,evaluated at \( x \), is the probability that \( X \) will take less than or equal to \(x \)

We can write it mathematically as

\( F_x (x) = P ( X \leq x ) \)

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